Question
A 7.00kg cannonball is traveling at a velocity of 75.0 m/s at a height of 80.0 m. What is its kinetic energy?
answers:
19,700 J
39,400 J
5500 J
525 J
answers:
19,700 J
39,400 J
5500 J
525 J
Answers
GPT-4o mini
To calculate the kinetic energy (KE) of the cannonball, you can use the kinetic energy formula:
\[
KE = \frac{1}{2} m v^2
\]
where:
- \( m \) is the mass of the object (in kg),
- \( v \) is the velocity of the object (in m/s).
Given:
- \( m = 7.00 \, \text{kg} \)
- \( v = 75.0 \, \text{m/s} \)
Substituting the values into the formula:
\[
KE = \frac{1}{2} \times 7.00 \, \text{kg} \times (75.0 \, \text{m/s})^2
\]
Calculating \( (75.0 \, \text{m/s})^2 \):
\[
75.0^2 = 5625 \, \text{m}^2/\text{s}^2
\]
Now substituting this back into the kinetic energy formula:
\[
KE = \frac{1}{2} \times 7.00 \, \text{kg} \times 5625 \, \text{m}^2/\text{s}^2
\]
Calculating:
\[
KE = \frac{1}{2} \times 7.00 \times 5625 = 3.5 \times 5625 = 19687.5 \, \text{J}
\]
Rounding to the appropriate significant figures, it is approximately:
\[
KE \approx 19700 \, \text{J}
\]
So the answer is:
**19,700 J**.
\[
KE = \frac{1}{2} m v^2
\]
where:
- \( m \) is the mass of the object (in kg),
- \( v \) is the velocity of the object (in m/s).
Given:
- \( m = 7.00 \, \text{kg} \)
- \( v = 75.0 \, \text{m/s} \)
Substituting the values into the formula:
\[
KE = \frac{1}{2} \times 7.00 \, \text{kg} \times (75.0 \, \text{m/s})^2
\]
Calculating \( (75.0 \, \text{m/s})^2 \):
\[
75.0^2 = 5625 \, \text{m}^2/\text{s}^2
\]
Now substituting this back into the kinetic energy formula:
\[
KE = \frac{1}{2} \times 7.00 \, \text{kg} \times 5625 \, \text{m}^2/\text{s}^2
\]
Calculating:
\[
KE = \frac{1}{2} \times 7.00 \times 5625 = 3.5 \times 5625 = 19687.5 \, \text{J}
\]
Rounding to the appropriate significant figures, it is approximately:
\[
KE \approx 19700 \, \text{J}
\]
So the answer is:
**19,700 J**.